However, in making cider, If I let the cider go from, say 70 to 00 and back sweeten with a can of frozen apple concentrate.. is there a way to figure what the ABV if I let it ferment just long enough to carbonate the bottles and then pasteurize in a hot water bath?

I'm guessing it won't raise the ABV much.. but, for the sake of MY science, I was hoping there was a way to calculate this out.

What if you let one of the bottles sit with an airlock or balloon so that it doesn't actually carb up, but would burn through the same ammount of sugar. Wouldn't gravity readings at bottling and then pasteurizing tell you how much ABV is raised, if it's even measurable. Unless I'm missing something.

Yes, it can be calculated approximately. Each 2.065 grams of extract (sugar) consumed produces 1.000 gram of ethanol. You can certainly calculate the total amount of sugar in the must (from the OG) and know how much you have added but you have to WAG the real degree of fermentation. The data from the yeast supplier should get you a rough estimate of this.

AJ is spot on quoting the balling observation. Another way to estimate ABV is to calculate an adjusted starting gravity by adding the shift the one can of apple juice concentrate adds. This can usually be figured out from the nutritional information.